Question

1) cos(x-1)=√3/2
2)cosx>√2/2 , x ∈ ( 0 ; π/2 )

Answer 1

$1) \: \cos(x - 1) = \frac{ \sqrt{3} }{2} \\ \\ a) \: x - 1 = \frac{\pi}{6} + 2\pi \: n \\ x = \frac{\pi}{6} + 1 + 2\pi \: n \\ \\ b) \: x - 1 = - \frac{\pi}{6} + 2\pi \: n \\ x = - \frac{\pi}{6} + 1 + 2\pi \: n$

n € Z

$2) \: \cos(x) > \frac{ \sqrt{2} }{2} \\ \\ - \frac{\pi}{4} + 2\pi \: n < x < \frac{\pi}{4} + 2\pi \: n$
n € Z